Make camera to move with animated object by makewalk
This problem is because armatures do not move objects, they move the vertices within the object. Think of objects like containers for their data. So your camera is behaving properly, because your object is not moving!

What you need is to attach the camera to a bone in the armature, not the object itself. Usually the Root bone is used for this, but it will vary. Look at your armature and pick a bone that is moving with the animation. As you are using mocap data, it may not be moving the root bone. If not, you could use one of the spine, hip, or pelvis bones. The key is to use one that isn't rotating, as that will rotate the camera.

To parent to a bone, select your object, then shift+select the bone and hit ctrl+P. (The armature needs to be in pose mode.) Alternatively, in the Object tab of the Properties Panel there is a Parent drop down menu that can be set to Bone, and then lets you pick the specific bone.

It is also possible to use constraints to attach the camera. This is more setup, but can let you do things like only copy a bone's translation, and not rotation.